{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Density of States\n",
    "# 1. Introduction\n",
    "- In this example, we calculate the phonon (vibrational) density of states (DOS) of graphene at 300 K and zero pressure. The method is based on the velocity auto-correlation (VAC) function. The DOS is calculated as the Fourier transform of the VAC [[Dickey 1969]](https://doi.org/10.1103/PhysRev.188.1407)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing Relevant Functions\n",
    "- The inputs/outputs for GPUMD are processed using the [Atomic Simulation Environment (ASE)](https://wiki.fysik.dtu.dk/ase/) and the [thermo](https://github.com/AlexGabourie/thermo) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import *\n",
    "from ase.build import graphene_nanoribbon\n",
    "from thermo.gpumd.data import load_dos, load_vac\n",
    "from thermo.gpumd.io import ase_atoms_to_gpumd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Preparing the Inputs\n",
    "- We use a sheet of graphene consisting of 8640 carbon atoms and use a Tersoff potential [[Tersoff 1989]](https://doi.org/10.1103/PhysRevB.39.5566) parameterized by Lindsay *et al.* [[Lindsay 2010]](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.81.205441).\n",
    "\n",
    "## Generate the  [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Atoms(symbols='C8640', pbc=[True, True, False], cell=[149.64918977395098, 155.52, 3.35])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gnr = graphene_nanoribbon(60, 36, type='armchair', sheet=True, vacuum=3.35/2, C_C=1.44)\n",
    "gnr.euler_rotate(theta=90)\n",
    "l = gnr.cell.lengths()\n",
    "gnr.cell = gnr.cell.new((l[0], l[2], l[1]))\n",
    "l = l[2]\n",
    "gnr.center()\n",
    "gnr.pbc = [True, True, False]\n",
    "gnr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ase_atoms_to_gpumd(gnr, M=3, cutoff=2.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The first few lines of the [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file are:\n",
    "```\n",
    "8640 3 2.1 0 0 0\n",
    "1 1 0 149.649 155.52 3.35\n",
    "0 1.24708 0 0 12\n",
    "0 0 0.72 0 12\n",
    "0 0 2.16 0 12\n",
    "0 1.24708 2.88 0 12\n",
    "```\n",
    "\n",
    "- Explanations for the first line:\n",
    "  - The first number states that the number of particles is 8640.\n",
    "  - The second number in this line, 3, is good for graphene described by the Tersoff potential because no atom can have more than 3 neighbor atoms at room temperature. Making this number larger only results in more memory usage. If this number is not large enough, GPUMD will give an error message and exit.\n",
    "  - The next number, 2.1, means that the initial cutoff distance for the neighbor list construction is 2.1 A. Here, we only need to consider the first nearest neighbors. Any number larger than the first nearest neighbor distance and smaller than the second nearest neighbor distance is OK here. Note that we will also not update the neighbor list. There is no such need in this problem. \n",
    "  - The remaining three zeros in the first line mean:\n",
    "    - the box is orthogonal;\n",
    "    - the initial velocities are not contained in this file;\n",
    "    - there are no grouping methods defined here.\n",
    "\n",
    "\n",
    " - Explanations for the second line:\n",
    "   - The numbers 1 1 0 mean that the $x$ and $y$ (in-plane) directions are periodic and the $z$ direction is open (free).\n",
    "   - The remaining three numbers are the box lengths in the three directions. The box length in a free direction is chosen based on some convention. This number will only affect the system volume.\n",
    "\n",
    "- Starting from the third line, the numbers in the first column are all 0 here, which means that all the atoms are of type 0 (single atom-type system). The next three columns are the initial coordinates of the atoms. The last column gives the masses of the atoms. Here, we consider isotopically pure C-12 crystal, but this Jupyter notebook will generate an [xyz.in](https://gpumd.zheyongfan.org/index.php/The_xyz.in_input_file) file using the average of the various isotopes of C. In some applications, one can consider mass disorder in a flexible way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The <code>run.in</code> file:\n",
    "The <code>run.in</code> input file is given below:<br>\n",
    "```\n",
    "potential   potentials/tersoff/Graphene_Lindsay_2010_modified.txt 0\n",
    "velocity    300\n",
    "\n",
    "ensemble    npt_ber 300 300 0.01 0 0 0 0.0005 \n",
    "time_step   1     \n",
    "dump_thermo 100     \n",
    "run         200000\n",
    "\n",
    "ensemble    nve \n",
    "compute_dos 5 200 400.0\n",
    "run         200000 \n",
    "```\n",
    " - The first line uses the [potential](https://gpumd.zheyongfan.org/index.php/The_potential_keyword) keyword to define the potential to be used, which is specified in the file [Graphene_Lindsay_2010_modified.txt](https://github.com/brucefan1983/GPUMD/blob/master/potentials/tersoff/Graphene_Lindsay_2010_modified.txt).\n",
    "\n",
    " - The second line uses the [velocity](https://gpumd.zheyongfan.org/index.php/The_velocity_keyword) keyword and sets the velocities to be initialized with a temperature of 300 K. \n",
    "\n",
    " - There are two runs:\n",
    "   - The first [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) serves as the equilibration stage, where the NPT [ensemble](https://gpumd.zheyongfan.org/index.php/The_ensemble_keyword) (the Berendsen method) is used. The temperature is 300 K and the pressures are zero in all the directions. The coupling constants are 0.01 (dimensionless) and 0.0005 (in the natural unit system adopted by GPUMD) for the thermostat and the barostat, respectively. The [time_step](https://gpumd.zheyongfan.org/index.php/The_time_step_keyword) for integration is 1 fs. There are $2\\times 10^5$ steps (200 ps) for this [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) and the thermodynamic quantities will be output every 1000 steps. \n",
    "   - The second [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) serves as the production [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword), where the NVE [ensemble](https://gpumd.zheyongfan.org/index.php/The_ensemble_keyword) is used. The line with [compute_dos](https://gpumd.zheyongfan.org/index.php/The_compute_dos_keyword) means that velocities will be recorded every 5 steps (5 fs) and 200 VAC data (the maximum correlation time is then about 1 ps) will be calculated. The last parameter in this line is the maximum angular frequency considered, $\\omega_{\\rm max} = 2\\pi\\nu_{\\rm max} =400$ THz, which is large enough for graphene. The production [run](https://gpumd.zheyongfan.org/index.php/The_run_keyword) lasts 200 ps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Results and Discussion\n",
    "### Computation Time\n",
    " - This simulation takes about 1.5 min when a Tesla K40 is used. \n",
    " -  The speed of this simulation is about $4\\times 10^7$ atom x step / second."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure Properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "aw = 2\n",
    "fs = 16\n",
    "font = {'size'   : fs}\n",
    "matplotlib.rc('font', **font)\n",
    "matplotlib.rc('axes' , linewidth=aw)\n",
    "\n",
    "def set_fig_properties(ax_list):\n",
    "    tl = 8\n",
    "    tw = 2\n",
    "    tlm = 4\n",
    "    \n",
    "    for ax in ax_list:\n",
    "        ax.tick_params(which='major', length=tl, width=tw)\n",
    "        ax.tick_params(which='minor', length=tlm, width=tw)\n",
    "        ax.tick_params(which='both', axis='both', direction='in', right=True, top=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot DOS and VAC\n",
    " - The [dos.out](https://gpumd.zheyongfan.org/index.php/The_dos.out_output_file) and [mvac.out](https://gpumd.zheyongfan.org/index.php/The_mvac.out_output_file) output files are loaded and processed to create the following figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DOS: dict_keys(['nu', 'DOSx', 'DOSy', 'DOSz', 'DOSxyz'])\n",
      "VAC: dict_keys(['t', 'VACx', 'VACy', 'VACz', 'VACxyz'])\n"
     ]
    }
   ],
   "source": [
    "Nc = 200\n",
    "dos = load_dos(num_dos_points=Nc)['run0']\n",
    "vac = load_vac(Nc)['run0']\n",
    "dos['DOSxyz'] = dos['DOSx']+dos['DOSy']+dos['DOSz']\n",
    "vac['VACxyz'] = vac['VACx']+vac['VACy']+vac['VACz']\n",
    "vac['VACxyz'] /= vac['VACxyz'].max() \n",
    "print('DOS:', dos.keys())\n",
    "print('VAC:', vac.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x720 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(12,10))\n",
    "subplot(2,2,1)\n",
    "set_fig_properties([gca()])\n",
    "plot(vac['t'], vac['VACx']/vac['VACx'].max(), color='C3',linewidth=3)\n",
    "plot(vac['t'], vac['VACy']/vac['VACy'].max(), color='C0', linestyle='--',linewidth=3)\n",
    "plot(vac['t'], vac['VACz']/vac['VACz'].max(), color='C2', linestyle='-.',zorder=100,linewidth=3)\n",
    "xlim([0,1])\n",
    "gca().set_xticks([0,0.5,1])\n",
    "ylim([-0.5, 1])\n",
    "gca().set_yticks([-0.5,0,0.5,1])\n",
    "ylabel('VAC (Normalized)')\n",
    "xlabel('Correlation Time (ps)')\n",
    "legend(['x','y', 'z'])\n",
    "title('(a)')\n",
    "\n",
    "subplot(2,2,2)\n",
    "set_fig_properties([gca()])\n",
    "plot(dos['nu'], dos['DOSx'], color='C3',linewidth=3)\n",
    "plot(dos['nu'], dos['DOSy'], color='C0', linestyle='--',linewidth=3)\n",
    "plot(dos['nu'], dos['DOSz'], color='C2', linestyle='-.',zorder=100, linewidth=3)\n",
    "xlim([0, 60])\n",
    "gca().set_xticks(range(0,61,20))\n",
    "ylim([0, 1500])\n",
    "gca().set_yticks(np.arange(0,1501,500))\n",
    "ylabel('PDOS (1/THz)')\n",
    "xlabel(r'$\\nu$ (THz)')\n",
    "legend(['x','y', 'z'])\n",
    "title('(b)')\n",
    "\n",
    "subplot(2,2,3)\n",
    "set_fig_properties([gca()])\n",
    "plot(vac['t'], vac['VACxyz'], color='k',linewidth=3)\n",
    "xlim([0,1])\n",
    "gca().set_xticks([0,0.5,1])\n",
    "ylim([-0.5, 1])\n",
    "gca().set_yticks([-0.5,0,0.5,1])\n",
    "ylabel('VAC (Normalized)')\n",
    "xlabel('Correlation Time (ps)')\n",
    "title('(c)')\n",
    "\n",
    "subplot(2,2,4)\n",
    "set_fig_properties([gca()])\n",
    "plot(dos['nu'], dos['DOSxyz'], color='k',linewidth=3)\n",
    "xlim([0, 60])\n",
    "gca().set_xticks(range(0,61,20))\n",
    "ylim([0, 2500])\n",
    "gca().set_yticks(np.arange(0,2501,500))\n",
    "ylabel('PDOS (1/THz)')\n",
    "xlabel(r'$\\nu$ (THz)')\n",
    "title('(d)')\n",
    "\n",
    "tight_layout()\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**(a)** Normalized VAC for individual directions. **(b)** DOS for individual directions. **(c)** Total Normalized VAC. **(d)** Total DOS."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - For 3D isotropic systems, the results along different directions are equivalent and can be averaged, but for 2D materials like graphene, it is natural to consider the in-plane part (the $x$ and $y$ directions in the simulation) and the out-of-plane part (the $z$ direction) separately. It can be seen that the two components behave very differently. We can see that the cutoff frequency for the out-of-plane component (about 40 THz) is smaller than that for the in-plane component (about 52 THz)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot Quantum-Corrected Heat Capacity\n",
    "\n",
    " - In classical MD simulations, the heat capacity per atom is almost $k_{\\rm B}$ even at temperatures that are much lower than the Debye temperature. With the DOS available, one can obtaine the following quantum heat capacity per atom in direction $\\alpha$:\n",
    "$$\n",
    "C_{\\alpha}(T) = \\int_0^{\\infty} \\frac{d\\omega}{2\\pi} \\rho_{\\alpha}(\\omega) \\frac{x^2 \\exp(x)}{(\\exp(x)-1)^2},\n",
    "$$\n",
    "where \n",
    "$$\n",
    "x=\\frac{\\hbar\\omega}{k_{\\rm B} T}\n",
    "$$\n",
    "and $\\rho_{\\alpha}(\\omega)$ is the density of states in direction $\\alpha$ normalized to 1:\n",
    "$$\n",
    "\\int_0^{\\infty} \\frac{d\\omega}{2\\pi} \\rho_{\\alpha}(\\omega) = 1.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "Temp = np.arange(100,5001,100)  # [K]\n",
    "N = 8640  # Number of atoms\n",
    "Cx, Cy, Cz = list(), list(), list()  # [k_B/atom] Heat capacity per atom\n",
    "hnu = 6.63e-34*dos['nu']*1.e12  # [J]\n",
    "\n",
    "for T in Temp:\n",
    "    kBT = 1.38e-23*T  # [J]\n",
    "    x = hnu/kBT\n",
    "    expr = np.square(x)*np.exp(x)/(np.square(np.expm1(x)))\n",
    "    Cx.append(np.trapz(dos['DOSx']*expr, dos['nu'])/N)\n",
    "    Cy.append(np.trapz(dos['DOSy']*expr, dos['nu'])/N)\n",
    "    Cz.append(np.trapz(dos['DOSz']*expr, dos['nu'])/N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(8,6))\n",
    "set_fig_properties([gca()])\n",
    "mew, ms, mfc, lw = 1, 8, 'none', 2.5\n",
    "plot(Temp, Cx, lw=lw,marker='d',mfc=mfc,ms=ms,mew=mew)\n",
    "plot(Temp, Cy, lw=lw,marker='s',mfc=mfc,ms=ms,mew=mew)\n",
    "plot(Temp, Cz, lw=lw,marker='o',mfc=mfc,ms=ms,mew=mew)\n",
    "xlim([0,5100])\n",
    "gca().set_xticks(range(0,5001,1000))\n",
    "ylim([0, 1.1])\n",
    "gca().set_yticks(np.linspace(0,1,6))\n",
    "ylabel(r'Heat Capacity (k$_B$/atom)')\n",
    "xlabel('Temperature (K)')\n",
    "legend(['x','y','z'])\n",
    "\n",
    "tight_layout()\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quantum heat capacity per atom as a function of temperature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - The above figure shows the calculated per-atom quantum heat capacity in different directions.\n",
    "\n",
    " - Again, the in-plane ($x$ and $y$ directions) and out-of-plane ($z$ direction) phonons behave differently.\n",
    "\n",
    " - For every direction, the quantum heat capacity increases from 0 to $k_{\\rm B}$ with increasing temperature.\n",
    "\n",
    " - One can also calculate the Debye temperature as a function of temperature $\\Theta(T)$, but we leave it to the reader."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. References\n",
    "- [Dickey 1969] J. M. Dickey and A. Paskin, [Computer Simulation of the Lattice Dynamics of Solids](https://doi.org/10.1103/PhysRev.188.1407), Phys. Rev. **188**, 1407 (1969).\n",
    "- [Lindsay 2010] L. Lindsay and D.A. Broido, [Optimized Tersoff and Brenner emperical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene](https://doi.org/10.1103/PhysRevB.39.5566), Phys. Rev. B, **81**, 205441 (2010).\n",
    "- [Tersoff 1989] J. Tersoff, [Modeling solid-state chemistry: Interatomic potentials for multicomponent systems](https://doi.org/10.1103/PhysRevB.39.5566), Phys. Rev. B **39**, 5566(R) (1989)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
